Differential and Integral Equations
- Differential Integral Equations
- Volume 13, Number 10-12 (2000), 1371-1392.
Modified motion by mean curvature: local existence and uniqueness and qualitative properties
We consider some free boundary problems involving motion by mean curvature and a nonlocal term. They arise as singular limits of various phase transition models. Using precise regularity estimates in Hölder spaces, we prove that these problems are well-posed. We study the qualitative behavior of the motion law and show in particular that the inclusion of interfaces is not preserved in time.
Differential Integral Equations, Volume 13, Number 10-12 (2000), 1371-1392.
First available in Project Euclid: 21 December 2012
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 35K55: Nonlinear parabolic equations
Secondary: 35A07 35B65: Smoothness and regularity of solutions 35R35: Free boundary problems 53C44: Geometric evolution equations (mean curvature flow, Ricci flow, etc.)
Bonami, A.; Hilhorst, D.; Logak, E. Modified motion by mean curvature: local existence and uniqueness and qualitative properties. Differential Integral Equations 13 (2000), no. 10-12, 1371--1392. https://projecteuclid.org/euclid.die/1356061130